A372454 a(n) = A372444(n) - A086893(1+A372449(n)).

6, -48, 2560, -1572864, -3848290697216, 6649092007880460460883968, -18999521285301737936647902825311679255527123058688, 76895533293152762966220781422103876125697362804839499718093497881599910128103059800826635129716736

Offset

0,1

Comments

The difference between A372444(n) and the term of A086893 with the same binary length.

Links

Antti Karttunen, Table of n, a(n) for n = 0..10

Formula

a(n) = A372444(n) - A086893(1+A000523(A372444(n))).

a(0) = A372453(0) = 6; and for n > 0, a(n) = 4^A372448(n-1) * A372453(n).

Example

The term of A086893 that has same binary length as A372444(0) = 27 is 21 [as 21 = 10101_2 in binary, and 27 = 11011_2 in binary], therefore a(0) = 27-21 = 6.
The term of A086893 that has same binary length as A372444(1) = 165 is 213, therefore a(1) = 165-213 = -48.

Prog

(PARI)
A000523(n) = logint(n, 2);
A371094(n) = { my(m=1+3*n, e=valuation(m, 2)); ((m*(2^e)) + (((4^e)-1)/3)); };
A372444(n) = { my(x=27); while(n, x=A371094(x); n--); (x); };
A086893(n) = (if(n%2, 2^(n+1), 2^(n+1)+2^(n-1))\3);
A372454(n) = { my(x=A372444(n)); (x - A086893(1+A000523(x))); };
(PARI) A372454(n) = if(!n, A372453(n), (4^A372448(n-1))*A372453(n));

Crossrefs

Cf. A000523, A086893, A372444, A372448, A372449, A372453.

Sequence in context: A192769 A324461 A084259 * A028308 A173011 A061429

Adjacent sequences: A372451 A372452 A372453 * A372455 A372456 A372457

Keyword

sign

Author

Antti Karttunen, May 05 2024

Status

approved